Loss functions for classification: Difference between revisions

Revision as of 22:11, 26 July 2019

Revision as of 22:35, 26 July 2019

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|<math>\arctan(v)+\frac{1}{2}</math>

|<math>\tan(\eta-\frac{1}{2})</math>

|}<br />The sole minimizer of the expected risk, <math>f^*_{\phi}</math>, associated with the above generated loss functions can be directly found from equation (1) and isshown to be equal to the corresponding <math>

f(\eta)

</math>. This holds even for the nonconvex loss functions which means that gradient descent based algorithms such as [[Gradient boosting|Gradient Boosting]] can be used to construct the minimizer in practice with finite training samples.